The Log Product Formula in quantum $K$-theory

Abstract

We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V\times W$ in terms of the invariants of $V$ and $W$. The proof requires introducing log virtual fundamental classes in $K$-theory and verifying their various functorial properties. We introduce a log version of $K$-theory and prove the formula there as well.

arXiv comment21 pages, comments welcome! v2: 27 pages, example added distinguishing log Gysin map from ordinary one

References in corpus (9)

• Quantum Cohomology of a Product
• The product formula for Gromov-Witten invariants
• Boundedness of the space of stable logarithmic maps
• The Log Product Formula
• Vanishing of the higher direct images of the structure sheaf
• K-theory and G-theory of derived algebraic stacks
• Vanishing theorems for the negative K-theory of stacks
• On a logarithmic version of the derived McKay correspondence
• On log motives

Cited by in corpus (2)

• A case study of intersections on blowups of the moduli of curves
• Higher Genus Quantum $K$--theory